No, Minoan gets you close to 5000, again depending on where you draw line. 5500 if you go back to its roots, hard to call that a civilization, maybe around 4500 if you're looking for something like precursor to cities in the form of small centers of trade. 4000 for examples of writing. Although with remains like that you never know if they simply used less durable materials before hand, or if none have been found yet.
Either way, on any of those benchmarks Mesopotamia precedes it by at least a few centuries or more, though Minoan does get you back pretty far. I don't know the migration patterns, but I think there was influence from Mesopotamia.
Classical Greece ~2500 years is probably often where the line is drawn because that's where some of the foundational works of culture, philosophy, and math had their start and became founding members of the "Western Canon". For millenia, students were trained in Greek and Latin and read the great works of those time periods. But there was a civilization that gradually evolved into that time period, complete with it's own Dark Ages before things climbed back up to what became Classical.
Either way, on any of those benchmarks Mesopotamia precedes it by at least a few centuries or more, though Minoan does get you back pretty far. I don't know the migration patterns, but I think there was influence from Mesopotamia.
Classical Greece ~2500 years is probably often where the line is drawn because that's where some of the foundational works of culture, philosophy, and math had their start and became founding members of the "Western Canon". For millenia, students were trained in Greek and Latin and read the great works of those time periods. But there was a civilization that gradually evolved into that time period, complete with it's own Dark Ages before things climbed back up to what became Classical.